Chapter 11, Problem 11.51P

Untapped geothermal sites in the United States havethe estimated potential to deliver $100,000\text{ MW}$ (electric) of new, clean energy. The key component in ageothermal power plant is a heat exchanger that transfers thermal energy from hot, geothermal brine to asecond fluid that is evaporated in the heat exchanger.The cooled brine is reinjected into the geothermal wellafter it exits the heat exchange, while the vapor exitingthe heat exchanger serves as the working fluid of aRankine cycle. Consider a geothermal power plant designed to deliver $P=25\text{ MW}$ (electric) operating ata thermal efficiency of $\eta =0.20$ . Pressurized hot brineat $T_{h,i}=200°C$ is sent w the tube side of a shell-and-tube heat exchanger, while the Rankine cycle’s working fluid enters the shell side at $T_{c,i}=45°C$ . The brineis reinjected into the well at $T_{h,o}=80°C$ .

(a) Assuming the brine has the properties of water, determine the required brine flow raw, the requiredeffectiveness of the heat exchanger, and therequired heat transfer surface area. The overall heat transfer coefficient is $U=4000{\text{ W/m}}^2$ .
(b) Over time, the brine fouls the heat transfer surfaces, resulting in $U=2000{\text{ W/m}}^2$ .For the operating conditions of part (a), determine the electricpower generated by the geothermal plant underfouled heat exchanger conditions.